There are generally two types of measurements made downhole—measurements of the rock surrounding the borehole (often referred to as formation evaluation) and measurements of the borehole and drilling assembly (often referred to as drilling monitoring). Examples of drilling monitoring include the following:                Angular displacement (DC magnetometer or gravimeter) or rotation speed (rate of change of angle, or directly derived from radial accelerometers) of the drillstring assembly, either above or below the motor.        Accelerations—measured using accelerometers, at each location along the drillstring there are 3 directions of linear acceleration, and one direction of rotational acceleration.        Strains—generally measured using combinations of strain gauges—such as weight, torque and bending moment. Also strain on components such as cutter lugs.        Pressures—absolute pressures measured inside and outside the drillstring and differential pressures, between the inside of the BHA and the annulus, or across the drilling motor or other downhole devices.        Speeds and torques of rotating components—such as turbines, drilling motors, mud pulsers.        Flow rates—generally these are inferred from other measurements such as turbine speed.        Temperatures—both mud temperatures inside and outside the drillstring, and component temperatures (such as bit bearings).        
Drilling monitoring data such as these as well as other types of drilling monitoring data generally have to be subjected to some form of data processing before transmission to the surface using while-drilling telemetry. Aside from just reducing the sampling rate to be compatible with the transmission rate, various means have been proposed for capturing some of the detail of the high frequency data in a few numbers that can be transmitted using available telemetry. Known processing techniques can consist of simple methods (such as mean, standard deviation, maximum and minimum) or more complicated procedures (spectra or wavelet analysis). The motivation for these procedures is the data bottleneck resulting from the slow telemetry rate from downhole to surface.
For example, U.S. Pat. No. 4,216,536 discloses calculating various properties (mean, positive and negative peaks, standard deviation, fundamental and harmonic frequencies and amplitudes), and transmitting a selection of these while drilling. U.S. Pat. No. 5,663,929 discloses the use of the wavelet transform to reduce the amount of data.
While both these types of methods serve the function of data reduction within in a single data channel, the usefulness of preserving high-frequency information that shows how different channels relate to one another was not appreciated. In general in the prior art it was not appreciated that one could capture information on the quantitative relationship between multiple channels at frequencies greatly in excess of the sampling rate.